Preheat oven to 400 degrees F.
Combine the chicken with the soy sauce, fish sauce, mirin, honey, and chili oil, tossing to coat. Let sit at room temperature for 20 minutes.
Meanwhile, make the sauce for the noodles. Heat 1 tablespoon oil in a medium sauce pot over medium heat. Add the serrano, garlic, and ginger and saute for 1 minute or until aromatic. Add the soy sauce, black vinegar, sugar, star anise, and a dash of white pepper. Bring the sauce to a boil, reduce heat and simmer for 2 minutes. Turn off the heat and let the sauce sit for 10 minutes. Strain, discarding the spices. Set aside.
Toss the broccoli with olive oil, curry powder, coriander, salt, and pepper. Lay the broccoli in an even layer on a baking sheet pan and roast for 20 minutes or until the stems are tender.
Line a baking sheet with aluminum foil or parchment paper. Lay the marinated chicken on the pan and roast for 20 minutes or until cooked. Let rest for 10 minutes, then slice into bite-size pieces.
Cook noodles according to the directions on the package. Drain and immediately toss the noodles with enough of the noodle sauce to season. You may not need all of the sauce. Portion the noodles into four bowls and top with the sliced chicken, roasted broccoli, sliced cucumber, crushed peanuts, and chopped cilantro. Serve immediately.